Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C32 |
No aliases for this group.
| Fitting, Sylow | H(5,𝔽3) ⋊ Q8 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, socle, hypercenter | C3 | #10620211 |
| commutator, prime radical, cosocle | #92404 | C22 |
| Fitting, hypocenter | H(5,𝔽3) | Q8 |
| LCS | G ▷ #92404 ▷ H(5,𝔽3) | |
| UCS | C1 ◁ C3 | |
220 conjugacy classes of subgroups.
| minimal degree | μ(G) = 27 |
| transitive degree | μt(G) = 27 |
Polycyclic presentation:
2^3,3^5|a^2=c,b^2=c,b^a=bc,d^a=de^2,e^a=d^2e^2,f^a=g,g^a=f^2,d^b=e,e^b=d^2,f^b=fg^2,g^b=f^2g^2,d^c=d^2,e^c=e^2,f^c=f^2,g^c=g^2,g^d=gh,f^e=fh,g^e=gh25 conjugacy classes — view the full character table.
| derived subgroup of | #72244504 |
| maximal subgroup of | #72209952, #72210394, #72214495, … |
| maximal normal subgroup of | #72209952, #72210394, #72214495, … |
| maximal quotient of | C2×#14519166, #72276147 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 3560);